Let $\lambda,\mu\in\mathbb{R}$. If the system of equations $3x+5y+\lambda z=3$ $7x+11y-9z=2$ $97x+155y-189z=\mu$ has infinitely many solutions, then $\mu+2\lambda$ is equal to:

1

The solution curve of the differential equation $2y\dfrac{dy}{dx}+3=5\dfrac{dy}{dx}$, passing through the point $(0,1)$…

Topic: JEE Main 2024 (9 April Morning Shift)

2

A variable line $L$ passes through the point $(3,5)$ and intersects the positive coordinate axes at the points $A$ and …

Topic: JEE Main 2024 (9 April Morning Shift)

3

The shortest distance between the lines $\dfrac{x - 3}{4} = \dfrac{y + 7}{-11} = \dfrac{z - 1}{5}$ and $\dfrac{x - 5}{3…

Topic: JEE Main 2024 (9 April Morning Shift)

4

Let $f(x) = x^{2} + 9$, $g(x) = \dfrac{x}{x - 9}$, and $a = f \circ g(10)$, $b = g \circ f(3)$. If $e$ and $l$ denote t…

Topic: JEE Main 2024 (9 April Morning Shift)

5

Let $\alpha, \beta$ be the roots of the equation $ x^{2} + 2\sqrt{2}x - 1 = 0 $. The quadratic equation whose roots are…

Topic: JEE Main 2024 (9 April Morning Shift)

6

Let $ \displaystyle \int \frac{2 - \tan x}{3 + \tan x} , dx = \frac{1}{2} \left( \alpha x + \log_e \left| \beta \sin x …

Topic: JEE Main 2024 (9 April Morning Shift)

7

Let a circle passing through $(2, 0)$ have its centre at the point $(h, k)$. Let $(x_c, y_c)$ be the point of intersect…

Topic: JEE Main 2024 (9 April Morning Shift)

8

The frequency distribution of the age of students in a class of 40 students is given below.If the mean deviation about …

Topic: JEE Main 2024 (9 April Morning Shift)

9

The coefficient of $x^{70}$ in $ x^{2}(1+x)^{98} + x^{3}(1+x)^{97} + x^{4}(1+x)^{96} + \dots + x^{54}(1+x)^{46} $ is $ …

Topic: JEE Main 2024 (9 April Morning Shift)

10

If the sum of the series $ \dfrac{1}{1(1+d)} + \dfrac{1}{(1+d)(1+2d)} + \dots + \dfrac{1}{(1+9d)(1+10d)} $ is equal to …

Topic: JEE Main 2024 (9 April Morning Shift)

1

A ray of light coming from the point $P(1,2)$ gets reflected from the point $Q$ on the $x$-axis and then passes through…

Topic: JEE Main 2024 (9 April Morning Shift)

2

Let the line $L$ intersect the lines $x-2=-y=z-1$, $2(x+1)=2(y-1)=z+1$ and be parallel to the line $\dfrac{x-2}{3}=\dfr…

Topic: JEE Main 2024 (9 April Morning Shift)

3

Let $\overrightarrow{OA}=2\vec a,\ \overrightarrow{OB}=6\vec a+5\vec b,\ \overrightarrow{OC}=3\vec b$, where $O$ is the…

Topic: JEE Main 2024 (9 April Morning Shift)